程序检查N是否为十进制数

给定数字N ，任务是检查N是否为十进制数。如果数字N是十进制数，则打印“是”，否则打印“否” 。

Decagonal Number is a figurate number that extends the concept of triangular and square numbers to the decagon (10-sided polygon). The nth decagonal numbers count the number of dots in a pattern of n nested decagons, all sharing a common corner, where the ith decagon in the pattern has sides made of i dots spaced one unit apart from each other. The first few decagonal numbers are 1, 10, 27, 52, 85, 126, 175, … 
 

例子：

Input: N = 10 
Output: Yes 
Explanation: 
Second decagonal number is 10.
Input: N = 30 
Output: No 
 

方法：

1. 十进制数的第K^个项为
   $K^{th} Term = 4*K^{2} - 3*K$
2. 由于我们必须检查给定的数字是否可以表示为十进制数。可以检查为：

=> $N = 4*K^{2} - 3*K$
=> $K = \frac{3 + \sqrt{16*N + 9}}{8}$
 

2. 如果使用上述公式计算的K值为整数，则N为十进制数。
3. 其他N不是十进制数。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to check if N is a
// Decagonal Number
bool isdecagonal(int N)
{
    float n
        = (3 + sqrt(16 * N + 9))
          / 8;
 
    // Condition to check if the
    // number is a decagonal number
    return (n - (int)n) == 0;
}
 
// Driver Code
int main()
{
    // Given Number
    int N = 10;
 
    // Function call
    if (isdecagonal(N)) {
        cout << "Yes";
    }
    else {
        cout << "No";
    }
    return 0;
}

Java

// Java program for the above approach
import java.lang.Math;
 
class GFG{
     
// Function to check if N is a
// decagonal number
public static boolean isdecagonal(int N)
{
    double n = (3 + Math.sqrt(16 * N + 9)) / 8;
     
    // Condition to check if the
    // number is a decagonal number
    return (n - (int)n) == 0;
}
 
// Driver code   
public static void main(String[] args)
{
         
    // Given number
    int N = 10;
     
    // Function call
    if (isdecagonal(N))
    {
        System.out.println("Yes");
    }
    else
    {
        System.out.println("No");
    }
}
}
 
// This code is contributed by divyeshrabadiya07

Python3

# Python3 program for the above approach
import math
 
# Function to check if N is a
# decagonal number
def isdecagonal(N):
 
    n = (3 + math.sqrt(16 * N + 9)) / 8
     
    # Condition to check if the
    # number is a decagonal number
    return (n - int(n)) == 0
     
# Driver Code
if __name__=='__main__':
     
    # Given number
    N = 10
     
    # Function Call
    if isdecagonal(N):
        print('Yes')
    else:
        print('No')
 
# This code is contributed by rutvik_56

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to check if N
// is a decagonal Number
static bool isdecagonal(int N)
{
    double n = (3 + Math.Sqrt(16 * N + 9)) / 8;
     
    // Condition to check if the
    // number is a decagonal number
    return (n - (int)n) == 0;
}
     
// Driver Code
static public void Main ()
{
     
    // Given Number
    int N = 10;
     
    // Function call
    if (isdecagonal(N))
    {
        Console.Write("Yes");
    }
    else
    {
        Console.Write("No");
    }
}
}
 
// This code is contributed by ShubhamCoder

Javascript

 
// javascript program for the above approach
 
 
// Function to check if N is a
// Decagonal Number
function isdecagonal( N)
{
    let n
        = (3 + Math.sqrt(16 * N + 9))
          / 8;
 
    // Condition to check if the
    // number is a decagonal number
    return (n - parseInt(n)) == 0;
}
 
 
// Driver Code
 
    // Given Number
    let N = 10;
 
    // Function Call
    if (isdecagonal(N)) {
        document.write( "Yes");
    }
    else {
        document.write( "No");
    }
 
// This code contributed by gauravrajput1
 

输出：

Yes